The human heart is a muscle-based organ divided into four chambers: two atria (top chambers holding the blood) and two ventricles (bottom thick-walled chambers meant to help pumping the blood into the circulatory system). When the myocardium and specialized fibers are resting, the heart collects de-oxygenated blood from the body in the right atrium and oxygenated blood from lungs in the left atrium. Then, with each heart beat (which results from a muscle contraction), the blood flows from the right ventricle into the lungs for oxygenation and from the left ventricle into the human body. This entire process of creating a heartbeat is known as the cardiac cycle and is carefully preceded and controlled by a complex electrical mechanism. As shown in FIG. 2, this activity can be recorded on an electrocardiogram as a P-wave (atrial depolarization), as well as QRS complex which corresponds to ventricles depolarization. The cardiac cycle ends with the ventricles repolarization, i.e., a small wave called the T-wave.
Because the R-waves are always the most pronounced ones on an electrocardiogram, the distance between two consecutive R waves (i.e., the R-R interval in FIG. 2) is used by physicians to determine the heart rate activity. Consequently, the study of heart rate variability is extremely important for medical diagnosis. This also motivates our optimal control approach seeking to regulate the magnitude of the R-R intervals and related electro-physiological signals.
Since their invention in 1932, implantable pacemakers have evolved from fixed rate pacemakers (i.e., medical devices delivering an electrical pulse at fixed intervals of time) and demand pacemakers (i.e., medical device triggering an electrical impulse only if a heartbeat is missing), to complex rate responsive pacemakers. The main distinction between the rate responsive pacemakers and their predecessors is that besides the sensory part responsible with sensing the heart beats, they also consist of a control part which is meant to adapt the pacing response as a function of the heart activity. Therefore, designing the control algorithm for heart pacing is a very important and challenging task. For instance, the introduction of extra pacing to an already active heart can be lethal because heart chambers will not have enough time to refill with blood and thus will not provide the necessary amount of oxygenated blood throughout the body. On the other hand, missing heart beats can also lead to critical conditions.
Consequently, based on the characteristics of the proposed control approaches and the state variables which are optimized, the rate responsive pacemakers can be classified as open loop, closed loop, metabolic, and autonomous nervous system (ANS) controllers. For instance, one approach describes a closed loop proportional (P) controller for optimal pacing, which maintains the venous oxygen saturation at a predefined level. Of note, the proposed P-controller relies on a postulated non-linear model that relates the venous oxygen saturation to the heart rate. Along the same lines, another approach discusses a closed loop pacing approach based on regulating the atrial-ventricular conduction time (AVCT). At the heart of its approach lies the assumption that the dynamics of AVCT can be modeled as a linear time invariant system. Employing a similar closed-loop process control, yet another approach proposes a classical proportional-integral derivative (PID) controller for ensuring that the entire system consisting of the heart rate activity and pacing pulse achieves a targeted R-R interval. More precisely, its PID controller uses the error difference between the monitored and the predefined target R-R interval to compute the necessary amplitude of the atrio-ventricular node vagal stimulation. Using the same error difference between the observed and targeted R-R interval, another approach proposes a proportional integral (PI) closed loop controller to determine the frequency of stimulation. Open loop pacing rate is determined only by the current state of heart rate by using a predefined model with no feedback from changes in the system and no observation of the output. Closed loop pacing rate is determined by using feedback information from the output of the systems (in particular, the heart rate activity). Metabolic pacing depends on metabolism and/or respiratory system. Autonomous nervous system pacing is influenced by the autonomous nervous system activity.
More recently, another approach assumes that the heart rate activity can be modeled by a second order transfer function and present a proportional plus derivative controller for regulating the heart rate.
A further approach proposes a nonlinear heart beat control algorithm that uses concepts of proportional gain and norm. Alternatively, one variant uses the fuzzy control theory to regulate pacing while patient respiratory rate and temperature are used as state variables. In contrast to these approaches, still another approach uses an optimal control approach to regulate the heart rate and the sympathetic activity while assuming that the blood pressure is the state variable.
Despite this significant body of work, current state-of-the-art pacing algorithms assume that the heart rate (and other relevant physiological processes) can be modeled via linear state equations. However, by relying on de-trended fluctuation analysis, one can observe that the R-R intervals exhibit a fractal behavior and thus cannot be well approximated by such linear models. To overcome this limitation, the present invention describes control algorithms of rate responsive pacemakers that rely on fractal dynamical equations using concepts from fractional calculus.